Finite Endpoint Connector Candidate and the Spatial Mapping-Fiber Gate
Record
Date: 2026-08-16
Status: proved for the finite integral connector presentation and for its conditional reduced parity consequence. The normalization-provenanced six-functor restriction into literal entry143 is not constructed, so the physical endpoint/Q mapping fiber and its class remain undefined. No graph admission is claimed.
Finite connector presentation
The ordinary six-chart KN corridor gluing obstruction of entry335 has three endpoint mismatches and three shifted-center mismatches. Adjoining one primitive candidate endpoint connector for each road, the three already available shifted-center homotopies, and the normalized W012 top filler gives seven nonzero Smith factors, all equal to one. The finite presentation is integral, has no denominator or torsion, and is compatible with the stated D3 and reflection permutations.
This is a candidate mapping-cone presentation, not a derivation of the endpoint connector maps. Its identity endpoint columns encode the required primitive boundary. A geometric proof still has to identify those columns with the normalization/log-excess source under an actual support-typed six-functor restriction to entry143.
Conditional parity calculation
If that missing restriction extends the intrinsic odd KN counit and the based qSigma comparison to entry158's pointed mapping fiber, the reduced endpoint row is [2,1]. Its Smith form is [1]. Positive normalization fixes the odd coordinate to one, so 2a+1=1 gives a=0. Under this hypothesis,
- p_partial,Q = 0 in H1(D3; Z_or);
- its polarity Bockstein is 0 in H2(D3; Z).
These are conditional consequences, not yet physical invariants. The four-term generic boundary [1,-1,-1,-1] is primitive and preserves the augmentation 3-1-1-1=0, but it does not itself construct the required restriction r_partial,Q.
Earliest remaining datum
Construct the normalization-provenanced support/nearby-cycle comparison r_partial,Q from the full source kernel to literal entry143, with the three endpoint connector columns, the three center homotopies, and the normalized generic qSigma top living in one Hom complex. Only after its chain, reflection, and endpoint framing squares are proved may the pointed mapping fiber be instantiated and the conditional zero promoted to physical p=0.
D8 and Jordan coherence remain downstream of that realization.
Executable evidence
Checkers:
research/voevodsky/check_dp6_global_kn_corridor_descent_no_go.rsSHA-25688180223b6c65e364fe086e1a9284ae523644d0b66be31359cc846bc01cd3e5eresearch/voevodsky/check_dp6_endpoint_q_mapping_fiber.rsSHA-256b5eb4a34f9426615cf6af40e24c91449ea92f780cc7354690f9d85669b039c3a
Rustfmt and warnings-denied metadata compilation passed for both checkers. The native linked runtime was not rerun in this increment.
Outcome contract
{
"claim": "The endpoint and center mismatch presentation admits a primitive torsion-free finite connector candidate; conditional on its missing spatial six-functor realization, the reduced endpoint/Q calculation gives p_partial_Q=0 and Bockstein=0.",
"status": "proved_scoped_finite_candidate_with_conditional_parity",
"finite_connector": {
"endpoint_columns": 3,
"center_homotopies": 3,
"top_fillers": 1,
"nonzero_smith_factors": [1, 1, 1, 1, 1, 1, 1]
},
"conditional_mapping_fiber": {
"row": [2, 1],
"smith": [1],
"p_partial_Q": 0,
"polarity_bockstein": 0
},
"physical_mapping_fiber_instantiated": false,
"physical_p_defined": false,
"minimal_additional_datum": "normalization-provenanced support/nearby-cycle restriction r_partial_Q deriving the endpoint, center, and generic-Q connector columns in literal entry143",
"unconstructed": [
"literal six-functor realization of endpoint connector columns",
"entry158 pointed endpoint/Q mapping fiber",
"physical p_partial_Q and Bockstein",
"D8 covariance of the instantiated fiber",
"Jordan coherence"
]
}